Sharpe Ratio Definition, Calculation, Quiz and Excel Tutorial

Understanding How to Apply the Sharpe Ratio to Investments

Intermediate

Sharpe Ratio is a widely-adopted return-to-risk ratio used to evaluate historical portfolio performance. It is also used in forward-looking portfolio optimizations with the objective of maximizing the Sharpe Ratio using forecasts.

How do you calculate the Sharpe Ratio? Start by subtracting the risk-free return from the portfolio return, then divide by the portfolio standard deviation. It was named after William F. Sharpe, a key contributor to the Capital Asset Pricing Model, in the 1960s.

Synonyms: Sharpe Index, Sharpe Measure

For context, if you take a moment to think about that measure more deeply, the numerator is return and the denominator is risk. So it measures the return of an investment per unit of risk. So the higher the better, right? More return for less risk is what we all want, economically too. More for less.

Of course you have to take into consideration the timeframes here, and we typically refer to them as historical, expected and forecast, where expected is the current market expectation, and the forecast is what an active manager forecasts in the future.

In a Sentence

Doc: The Sharpe Ratio influenced two different fields in Finance. So Bill sure was sharp.
Joe: Excuse me, Professor. Was that supposed to be funny?

Video

This video can be accessed in a new window or App , at the YouTube Channel or from below.

Sharpe Ratio definition for investment modeling (4:34)

Video Script

The script includes two sections where we visualize and demonstrate the concept of the Sharpe Ratio.

Visualize

We're sitting in Excel and this is a snippet from our boot camp course.

Here we are focused on portfolios and specifically evaluating the historical performance of portfolios. See the video on portfolio optimization for related forward-looking concepts.

This method is called returns-based performance analysis, meaning we are taking monthly returns as the input. Holdings-based performance analysis uses holdings and provides more detail, but is too complex to cover here.

First, we need to create a portfolio. In this section we have a Market portfolio, like an index or benchmark, with these weights to four stocks, and another called Portfolio which is actively managed, with these weights. Active weights refer to the differences.

Here we have returns calculated over a 60-month period, totals and averages, based on data on the Returns tab. Let's focus on the second row, average arithmetic. The Portfolio beat the Market by 0.08% per month.

Next we have the standard deviation of monthly returns, so the Portfolio had higher monthly volatility.

While not required for the Sharpe Ratio, it is a good idea to run a regression, as shown on this chart, the 60 monthly returns on the Market plotted on the x-axis with the Portfolio return on the y-axis. So from the regression we get the measures alpha and beta here.

And last, this section we have the formula for the Sharpe Ratio, the risk-free rate of 0.24% and a table for the calculation of several ratios.

Next, let's focus on this cell G28 and demonstrate.

Demonstrate

This is one way to calculate the Sharpe Ratio in Excel, using monthly data but it is very common to use annual figures.

Ok, we have all the data we need. Using this formula, let's take the Portfolio return 0.79%, minus the risk-free of 0.24%, then divide by 5.30% to get 0.104. This is low, as Sharpe Ratios above 1.0 are considered good.

The Sharpe Ratio can be thought of as the slope of a line too, with a higher sloping line offering a higher reward-to-risk ratio, which is better. And remember, this can be negative as well.

Quiz

Click box for answer.

The Sharpe Ratio can be interpreted as the slope of a line. | True or False?

True

A manager has a long-term Sparpe Ratio of 0.75. Is it possible for that manager to still be underperforming her benchmark? | Yes or No?

Yes, neither return nor risk measure a benchmark.

Questions or Comments?

Still unclear on the Sharpe Ratio? Leave a question in the comments section on YouTube or check out the Quant 101 Series, specifically Analyze portfolio performance with linear regression in Excel.

Related Terms

Our trained humans found other terms in the category risk-adjusted performance you may find helpful.